Find the Tangent Line at the Point y=2x^3-4x , (1,-2)

Problem

y=2*x3−4*x,(1,−2)

Solution

1. Find the derivative of the function to determine the slope of the tangent line at any point x

d(y)/d(x)=6*x2−4

2. Evaluate the derivative at the given point x=1 to find the specific slope m

m=6*(1)2−4

m=2

3. Use the point-slope formula y−(y_1)=m*(x−(x_1)) with the point (1,−2) and the slope m=2

y−(−2)=2*(x−1)

4. Simplify the equation into slope-intercept form y=m*x+b

y+2=2*x−2

y=2*x−4

Final Answer

y=2*x−4

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